A Superconvergence result for mixed finite element approximations of the eigenvalue problem∗

Qun Lin; Hehu Xie

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 4, page 797-812
  • ISSN: 0764-583X

Abstract

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In this paper, we present a superconvergence result for the mixed finite element approximations of general second order elliptic eigenvalue problems. It is known that a superconvergence result has been given by Durán et al. [Math. Models Methods Appl. Sci. 9 (1999) 1165–1178] and Gardini [ESAIM: M2AN 43 (2009) 853–865] for the lowest order Raviart-Thomas approximation of Laplace eigenvalue problems. In this work, we introduce a new way to derive the superconvergence of general second order elliptic eigenvalue problems by general mixed finite element methods which have the commuting diagram property. Some numerical experiments are given to confirm the theoretical analysis.

How to cite

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Lin, Qun, and Xie, Hehu. "A Superconvergence result for mixed finite element approximations of the eigenvalue problem∗." ESAIM: Mathematical Modelling and Numerical Analysis 46.4 (2012): 797-812. <http://eudml.org/doc/222158>.

@article{Lin2012,
abstract = {In this paper, we present a superconvergence result for the mixed finite element approximations of general second order elliptic eigenvalue problems. It is known that a superconvergence result has been given by Durán et al. [Math. Models Methods Appl. Sci. 9 (1999) 1165–1178] and Gardini [ESAIM: M2AN 43 (2009) 853–865] for the lowest order Raviart-Thomas approximation of Laplace eigenvalue problems. In this work, we introduce a new way to derive the superconvergence of general second order elliptic eigenvalue problems by general mixed finite element methods which have the commuting diagram property. Some numerical experiments are given to confirm the theoretical analysis.},
author = {Lin, Qun, Xie, Hehu},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Second order elliptic eigenvalue problem; mixed finite element method; superconvergence; second-order elliptic eigenvalue problem; eigenfunction approximation; lowest-order Raviart-Thomas approximation; numerical experiments},
language = {eng},
month = {2},
number = {4},
pages = {797-812},
publisher = {EDP Sciences},
title = {A Superconvergence result for mixed finite element approximations of the eigenvalue problem∗},
url = {http://eudml.org/doc/222158},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Lin, Qun
AU - Xie, Hehu
TI - A Superconvergence result for mixed finite element approximations of the eigenvalue problem∗
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/2//
PB - EDP Sciences
VL - 46
IS - 4
SP - 797
EP - 812
AB - In this paper, we present a superconvergence result for the mixed finite element approximations of general second order elliptic eigenvalue problems. It is known that a superconvergence result has been given by Durán et al. [Math. Models Methods Appl. Sci. 9 (1999) 1165–1178] and Gardini [ESAIM: M2AN 43 (2009) 853–865] for the lowest order Raviart-Thomas approximation of Laplace eigenvalue problems. In this work, we introduce a new way to derive the superconvergence of general second order elliptic eigenvalue problems by general mixed finite element methods which have the commuting diagram property. Some numerical experiments are given to confirm the theoretical analysis.
LA - eng
KW - Second order elliptic eigenvalue problem; mixed finite element method; superconvergence; second-order elliptic eigenvalue problem; eigenfunction approximation; lowest-order Raviart-Thomas approximation; numerical experiments
UR - http://eudml.org/doc/222158
ER -

References

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